Primitive ideals of $\mathrm{U}(\mathfrak{s}\mathfrak{l}(\mathrm{\infty }))$ and the Robinson-Schensted algorithm at infinity

We present an algorithm which computes the annihilator in ${\rm U}(\frak{sl}(\infty))$ofanysimplehighestweight$\frak{sl}(\infty)$-module$L_\frak b(\lambda)$. This algorithm is based on an infinite version of the Robinson-Schensted algorithm.